Jimmy is a mental patient.
Think about it. Even without the talking cartoons, nothing about the movie, or by extension the show, makes sense. Alien sister? Come on! He was committed, but then the mental hospital just made him more unhinged. The reason for the race lift of those two friends of his: they were fellow patients that he projected into his delusions. The two that were portrayed by the Asian actors were successfully treated, so he just started projecting onto two newcomers. This also works for why he begins to see the Applegate characters: Robin was committed for being an obsessive fan that eventually snapped. He integrates the Applegate characters into his crazy after talking to her. The brain surgery was actually an (unsuccessful) attempt at some sort of treatment. As for why the series was so bad: again he's getting worse and worse. The entire series is All Just a Dream.
The train that hit Jimmy at the beginning of the movie left him comatose, and the entire series is his dream, hence the nonsensical things that happen in the series, the alien sister is a result of Jimmy's subconscious, she was actually a normal human teenager dressed up for a sci-fi convention that she was going to that day when Jimmy was hit by the train, the cartoon characters are spirit guides also created by his subconscious, as a way of guiding Jimmy out of his coma and back into the real world. The cartoons are actually a Stand that manifests as many different entities.
Nobody else can see them because there are no other Stand users around town, and they have a limited influence over the world aside from Jimmy himself because he is inexperienced with them, doesn't understand their true nature, and they're just not really that powerful in the first place. The cartoons actually do exist out of Jimmy's imagination.
- They're simply Invisible to Normals, and Appleday was the only one who could see them. There may be even more cartoons out there, it's just that they're the ones Appleday met and decided to make a show out of it. As no one would believe Appleday, he and the cartoons just resigned themselves to believe they didn't exist aside from imaginary creatures.
Appleday was schizophrenic.
Sure, he channeled it creatively, but he still went about talking to his hallucinations. Some might have thought he was an eccentric genius, and let his bizarre behavior pass, but, c'mon, the guy drank paint—which eventually killed him—and gave his Mouseketeer knockoffs a lifetime contract, which means they were working well into their dotage. Also, mental illness is hereditary, which could explain much about Sonny. They really missed an opportunity not giving Yancey her own spin-off.
Cute green alien girl, taken in by an eccentric human family, snarky disposition, hates Earth food, has "lame" powers, lives with a schizophrenic boarder who constantly tries to murder her adoptive brother? She's the real draw here.